Download Document 8910353

Hints for Capacitor Circuit Exercises 2.1, 2.2 and 3 Basic Idea: Apply the rules for parallel and serial combinaAon of capacitances, as summarized on the next page, to analyze the capacitor circuits in Exercises 2.1, 2.2 and 3. AddiAonal, detailed step-­‐by-­‐step Hints for Exercise 3 are given below. Remember the rules for parallel and serial combinaAon of capacitors, C1 and C2: Parallel: C1 a1 +Q1 Q12 Voltage Drops: V1 = Va1 – Vb1 , V2 = Va2 – Vb2 , V12 = Va – Vb b1 -­‐Q1 Charges: Q1 = C1 V1 , Q2 = C2 V2 Q12 a b +Q2 -­‐Q2 a2 C2 Charges Add Up: Q1 + Q2 = Q12 Equivalent Capacitance C12: C12 = Q12 / V12 è C12 = C1 + C2 b2 Voltage Drops: V1 = Va – Vb , V2 = Vb – Vc , V12 = Va – Vc Serial: C1 Q12 a Voltage Drops are Equal: V1 = V2 = V12 C2 Q12 b +Q1 -­‐Q1 +Q2 Charges: Q1 = C1 V1 , Q2 = C2 V2 -­‐Q2 c Voltage Drops Add Up: V1 + V2 = V12 Charges are Equal: Q1 = Q2 = Q12 Equivalent Capacitance C12: C12 = Q12 / V12 è 1/C12 = 1/C1 + 1/C2 Hints for Capacitor Circuit Exercise 3, Part (a) Basic Idea: Simplify the circuit, step by step, by successively replacing parallel or serial capacitor combinaAons by their respecAve equivalent capacitances, going from the complicated original circuit, Circuit O, to a final circuit, Circuit 3, which will contain only one single equivalent capacitance, connected directly to the baVery: Circuit O à Circuit 1 à Circuit 2 à Circuit 3 Replace 3μF and 5μF capacitors by their equivalent, C35 ; Replace 2μF and 4μF capacitors by their equivalent, C24 . Circuit O What is C35? What is C24? C35 C24 Circuit O Replace 8μF and C35 capacitors by their equivalent, C835 ; Replace C24 and 6μF capacitors by their equivalent, C246 . C35 C24 Circuit 1 What is C835? What is C246? C35 C835 C24 C246 Circuit 1 Replace C835 and C246 capacitors by their equivalent, Ceq . C835 CC246
246
Circuit 2 What is Ceq ? C835 Ceq CC246
246
Circuit 2 Ceq is connected directly to the baVery è By definiAon: Ceq = Q / Vb è Q = Ceq Vb Ceq C246 Circuit 3 Hints for Capacitor Circuit Exercise 3, Part (b) Basic Idea: Step by step, going backwards from Circuit 3 à Circuit 2 à Circuit 1 à Circuit 0, restore original capacitor components from the resp. equivalent capacitances. Use the parallel or serial capacitor combinaAon rules to infer the voltage drops and charges on original capacitor components from the charges stored and voltage drops across the respecAve equivalent capacitances. C835 and C246 are connected in parallel à voltage drops V835 and V246 are equal V835 = V246 = Vb = 20V è  Can calculate charges Q835 and Q246 : Q835 = C835 V835 = C835 Vb and Q246 = C246 V246 = C246 Vb Check: Is Q835 + Q246 = Q ? C835 Q +Q835 -­‐ Q835 +Q246 -­‐ Q246 CC246
246
Q Circuit 2 C8 = 8μF and C35 are in series à charges Q8 and Q35 are equal Q8 = Q35 = Q835 = …(see above)… è  Can calculate voltage drops V8 and V35 : V8 = Q8 / C8 = Q835 / C8 and V35 = Q35 / C35 = Q835 / C35 C24 and C6 = 6μF are in series à charges Q24 and Q6 are equal Q24 = Q6 = Q246 = …(see above)… è  Can calculate voltage drops V24 and V6 : V24 = Q24 / C24 = Q246 / C6 and V6 = Q6 / C6 = Q246 / C6 Q835 C35 +Q8 -­‐ Q8 Q246 -­‐ Q35 C24 +Q24 Q +Q35 -­‐ Q24 Check: Is V8 + V35 = V835 = Vb ? Is V24 + V6 = V246 = Vb ? Q835 Q246 +Q6 -­‐ Q6 Q Circuit 1 C5 =5μF and C3 = 3μF are connected in parallel à voltage drops V5 and V3 are equal V5 = V3 = V35 = …(see above)… è  Can calculate charges Q5 and Q3 : Q5 = C5 V5 = C5 V35 and Q3 = C3 V3 = C3 V35 C2 = 2μF and C4 = 4μF are connected in parallel à voltage drops V2 and V4 are equal V2 = V4 = V24 = …(see above)… è  Can calculate charges Q2 and Q4 : Q2 = C2 V2 = C2 V24 and Q4 = C4 V4 = C4 V24 Q35 +Q5 -­‐ Q5 Q35 Check: Is Q5 + Q3 = Q35 ? Is Q2 + Q4 = Q24 ? +Q3 -­‐ Q3 Q24 Q +Q2 -­‐ Q2 +Q4 -­‐ Q4 Q24 Q Circuit O